Why can't I see the FBX version to which I want to export to?
Blender 2.79b

Blender 2.79.7 didn't have this feature. You need to update to a more recent version of Blender. A more recent version can be installed along-side your current Blender version. The UI option for the export in 2.79b is depicted in the following image:





Blender 2.8x

Blender 2.80 and later only support the FBX 7.x binary format. The FBX ASCII format was removed in commit 7f50cbf2b6bf0675e4a178cbb19aca90f39bd374. Exporter options can be found in the sidebar of the file browser. In case they aren't displayed by default,  click on the gear icon to toggle the visibility of the sidebar.